%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SCT261_5 : TPTP v9.2.0. Released v6.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n001.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Fri Oct 3 07:59:19 PM UTC 2025 % Result : Theorem 12.16s 12.32s % Output : Proof 12.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SCT261_5 : TPTP v9.2.0. Released v6.0.0. % 0.06/0.13 % Command : duper %s % 0.14/0.34 % Computer : n001.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Thu Oct 2 21:01:08 EDT 2025 % 0.14/0.34 % CPUTime : % 12.16/12.32 SZS status Theorem for theBenchmark.p % 12.16/12.32 SZS output start Proof for theBenchmark.p % 12.16/12.32 Clause #8 (by assumption #[]): Eq % 12.16/12.32 (member (product_prod arrow_411405190le_alt arrow_411405190le_alt) % 12.16/12.32 (product_Pair arrow_411405190le_alt arrow_411405190le_alt a b) % 12.16/12.32 (aa (fun arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.32 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) f % 12.16/12.32 (combc arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.32 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.32 (combc arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.32 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.32 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.32 (combb bool % 12.16/12.32 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.32 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.32 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool))) % 12.16/12.32 arrow_159774573e_indi (if (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.32 (combc arrow_159774573e_indi nat bool (combb nat (fun nat bool) arrow_159774573e_indi (ord_less nat) h) % 12.16/12.32 (plus_plus nat n (one_one nat)))) % 12.16/12.32 lab) % 12.16/12.32 lba))) % 12.16/12.32 True % 12.16/12.32 Clause #9 (by assumption #[]): Eq % 12.16/12.32 (Iff % 12.16/12.32 (member (product_prod arrow_411405190le_alt arrow_411405190le_alt) % 12.16/12.32 (product_Pair arrow_411405190le_alt arrow_411405190le_alt c e) % 12.16/12.32 (aa (fun arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.32 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) f % 12.16/12.32 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.32 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.32 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.32 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.32 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.32 (combb bool % 12.16/12.32 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.32 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.32 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool))) % 12.16/12.32 arrow_159774573e_indi (if (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.32 (combc arrow_159774573e_indi nat bool (combb nat (fun nat bool) arrow_159774573e_indi (ord_less nat) h) % 12.16/12.32 n)) % 12.16/12.32 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.16/12.32 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.32 (combb (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.32 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.32 arrow_159774573e_indi arrow_424895264_mktop p) % 12.16/12.32 e)) % 12.16/12.32 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.32 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.32 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.32 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.32 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.32 (combb bool % 12.16/12.32 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.32 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.32 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool))) % 12.16/12.32 arrow_159774573e_indi (if (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.33 (combc arrow_159774573e_indi nat bool (combb nat (fun nat bool) arrow_159774573e_indi (fequal nat) h) % 12.16/12.33 n)) % 12.16/12.33 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.16/12.33 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.33 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.16/12.33 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.33 (combb (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.33 (fun arrow_411405190le_alt % 12.16/12.33 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool))) % 12.16/12.33 arrow_159774573e_indi arrow_1158827142_above p) % 12.16/12.33 c) % 12.16/12.33 e)) % 12.16/12.33 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.16/12.33 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.33 (combb (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.33 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.33 arrow_159774573e_indi arrow_276188178_mkbot p) % 12.16/12.33 e))))) % 12.16/12.33 (member (product_prod arrow_411405190le_alt arrow_411405190le_alt) % 12.16/12.33 (product_Pair arrow_411405190le_alt arrow_411405190le_alt a b) % 12.16/12.33 (aa (fun arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.33 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) f % 12.16/12.33 (combc arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.33 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.33 (combc arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.33 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.33 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.33 (combb bool % 12.16/12.33 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.33 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.33 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool))) % 12.16/12.33 arrow_159774573e_indi (if (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.33 (combc arrow_159774573e_indi nat bool (combb nat (fun nat bool) arrow_159774573e_indi (ord_less nat) h) % 12.16/12.33 (plus_plus nat n (one_one nat)))) % 12.16/12.33 lab) % 12.16/12.33 lba)))) % 12.16/12.33 True % 12.16/12.33 Clause #116 (by assumption #[]): Eq % 12.16/12.33 (Not % 12.16/12.33 (member (product_prod arrow_411405190le_alt arrow_411405190le_alt) % 12.16/12.33 (product_Pair arrow_411405190le_alt arrow_411405190le_alt c e) % 12.16/12.33 (aa (fun arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.33 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) f % 12.16/12.33 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.33 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.33 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.33 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.33 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.33 (combb bool % 12.16/12.33 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.33 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.33 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool))) % 12.16/12.33 arrow_159774573e_indi (if (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.33 (combc arrow_159774573e_indi nat bool (combb nat (fun nat bool) arrow_159774573e_indi (ord_less nat) h) % 12.16/12.34 n)) % 12.16/12.34 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.16/12.34 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.34 (combb (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.34 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.34 arrow_159774573e_indi arrow_424895264_mktop p) % 12.16/12.34 e)) % 12.16/12.34 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.34 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.34 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.34 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.34 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.34 (combb bool % 12.16/12.34 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.34 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.34 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool))) % 12.16/12.34 arrow_159774573e_indi (if (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.34 (combc arrow_159774573e_indi nat bool (combb nat (fun nat bool) arrow_159774573e_indi (fequal nat) h) % 12.16/12.34 n)) % 12.16/12.34 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.16/12.34 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.34 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.16/12.34 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.34 (combb (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.34 (fun arrow_411405190le_alt % 12.16/12.34 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool))) % 12.16/12.34 arrow_159774573e_indi arrow_1158827142_above p) % 12.16/12.34 c) % 12.16/12.34 e)) % 12.16/12.34 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.16/12.34 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.34 (combb (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.34 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.34 arrow_159774573e_indi arrow_276188178_mkbot p) % 12.16/12.34 e)))))) % 12.16/12.34 True % 12.16/12.34 Clause #215 (by clausification #[9]): Or % 12.16/12.34 (Eq % 12.16/12.34 (member (product_prod arrow_411405190le_alt arrow_411405190le_alt) % 12.16/12.34 (product_Pair arrow_411405190le_alt arrow_411405190le_alt c e) % 12.16/12.34 (aa (fun arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.34 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) f % 12.16/12.34 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.34 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.34 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.34 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.34 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.34 (combb bool % 12.16/12.34 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.34 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.34 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool))) % 12.16/12.34 arrow_159774573e_indi (if (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.34 (combc arrow_159774573e_indi nat bool (combb nat (fun nat bool) arrow_159774573e_indi (ord_less nat) h) % 12.16/12.34 n)) % 12.16/12.34 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.16/12.35 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (combb (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.35 arrow_159774573e_indi arrow_424895264_mktop p) % 12.16/12.35 e)) % 12.16/12.35 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.35 (combb bool % 12.16/12.35 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool))) % 12.16/12.35 arrow_159774573e_indi (if (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.35 (combc arrow_159774573e_indi nat bool (combb nat (fun nat bool) arrow_159774573e_indi (fequal nat) h) % 12.16/12.35 n)) % 12.16/12.35 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.16/12.35 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.16/12.35 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.35 (combb (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun arrow_411405190le_alt % 12.16/12.35 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool))) % 12.16/12.35 arrow_159774573e_indi arrow_1158827142_above p) % 12.16/12.35 c) % 12.16/12.35 e)) % 12.16/12.35 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.16/12.35 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (combb (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.35 arrow_159774573e_indi arrow_276188178_mkbot p) % 12.16/12.35 e))))) % 12.16/12.35 True) % 12.16/12.35 (Eq % 12.16/12.35 (member (product_prod arrow_411405190le_alt arrow_411405190le_alt) % 12.16/12.35 (product_Pair arrow_411405190le_alt arrow_411405190le_alt a b) % 12.16/12.35 (aa (fun arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.35 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) f % 12.16/12.35 (combc arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (combc arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.35 (combb bool % 12.16/12.35 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool))) % 12.16/12.35 arrow_159774573e_indi (if (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.35 (combc arrow_159774573e_indi nat bool (combb nat (fun nat bool) arrow_159774573e_indi (ord_less nat) h) % 12.16/12.35 (plus_plus nat n (one_one nat)))) % 12.16/12.35 lab) % 12.16/12.35 lba))) % 12.16/12.35 False) % 12.16/12.35 Clause #217 (by forward demodulation #[215, 8]): Or % 12.16/12.35 (Eq % 12.16/12.35 (member (product_prod arrow_411405190le_alt arrow_411405190le_alt) % 12.16/12.35 (product_Pair arrow_411405190le_alt arrow_411405190le_alt c e) % 12.16/12.35 (aa (fun arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.35 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) f % 12.16/12.35 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.35 (combb bool % 12.16/12.35 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool))) % 12.16/12.35 arrow_159774573e_indi (if (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.35 (combc arrow_159774573e_indi nat bool (combb nat (fun nat bool) arrow_159774573e_indi (ord_less nat) h) % 12.16/12.35 n)) % 12.16/12.35 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.16/12.35 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (combb (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.35 arrow_159774573e_indi arrow_424895264_mktop p) % 12.16/12.35 e)) % 12.16/12.35 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.35 (combb bool % 12.16/12.35 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool))) % 12.16/12.35 arrow_159774573e_indi (if (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.35 (combc arrow_159774573e_indi nat bool (combb nat (fun nat bool) arrow_159774573e_indi (fequal nat) h) % 12.16/12.35 n)) % 12.16/12.35 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.16/12.35 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.16/12.35 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.35 (combb (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun arrow_411405190le_alt % 12.16/12.35 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool))) % 12.16/12.35 arrow_159774573e_indi arrow_1158827142_above p) % 12.16/12.35 c) % 12.16/12.35 e)) % 12.16/12.35 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.16/12.35 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (combb (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.16/12.35 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.16/12.35 arrow_159774573e_indi arrow_276188178_mkbot p) % 12.16/12.35 e))))) % 12.16/12.35 True) % 12.16/12.35 (Eq True False) % 12.16/12.35 Clause #218 (by clausification #[217]): Eq % 12.16/12.35 (member (product_prod arrow_411405190le_alt arrow_411405190le_alt) % 12.16/12.35 (product_Pair arrow_411405190le_alt arrow_411405190le_alt c e) % 12.22/12.36 (aa (fun arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.22/12.36 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) f % 12.22/12.36 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.36 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.36 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.36 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.36 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.22/12.36 (combb bool % 12.22/12.36 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.36 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.36 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool))) % 12.22/12.36 arrow_159774573e_indi (if (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.22/12.36 (combc arrow_159774573e_indi nat bool (combb nat (fun nat bool) arrow_159774573e_indi (ord_less nat) h) n)) % 12.22/12.36 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.22/12.36 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.36 (combb (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.36 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.22/12.36 arrow_159774573e_indi arrow_424895264_mktop p) % 12.22/12.36 e)) % 12.22/12.36 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.36 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.36 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.36 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.36 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.22/12.36 (combb bool % 12.22/12.36 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.36 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.36 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool))) % 12.22/12.36 arrow_159774573e_indi (if (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.22/12.36 (combc arrow_159774573e_indi nat bool (combb nat (fun nat bool) arrow_159774573e_indi (fequal nat) h) n)) % 12.22/12.36 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.22/12.36 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.36 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.22/12.36 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.22/12.36 (combb (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.36 (fun arrow_411405190le_alt % 12.22/12.36 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool))) % 12.22/12.36 arrow_159774573e_indi arrow_1158827142_above p) % 12.22/12.36 c) % 12.22/12.36 e)) % 12.22/12.36 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.22/12.36 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.36 (combb (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.36 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.22/12.36 arrow_159774573e_indi arrow_276188178_mkbot p) % 12.22/12.36 e))))) % 12.22/12.36 True % 12.22/12.36 Clause #4405 (by clausification #[116]): Eq % 12.22/12.36 (member (product_prod arrow_411405190le_alt arrow_411405190le_alt) % 12.22/12.36 (product_Pair arrow_411405190le_alt arrow_411405190le_alt c e) % 12.22/12.36 (aa (fun arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.22/12.36 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) f % 12.22/12.36 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.38 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.38 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.38 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.38 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.22/12.38 (combb bool % 12.22/12.38 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.38 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.38 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool))) % 12.22/12.38 arrow_159774573e_indi (if (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.22/12.38 (combc arrow_159774573e_indi nat bool (combb nat (fun nat bool) arrow_159774573e_indi (ord_less nat) h) n)) % 12.22/12.38 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.22/12.38 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.38 (combb (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.38 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.22/12.38 arrow_159774573e_indi arrow_424895264_mktop p) % 12.22/12.38 e)) % 12.22/12.38 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.38 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.38 (combs arrow_159774573e_indi (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.38 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.38 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.22/12.38 (combb bool % 12.22/12.38 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.38 (fun (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.38 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool))) % 12.22/12.38 arrow_159774573e_indi (if (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.22/12.38 (combc arrow_159774573e_indi nat bool (combb nat (fun nat bool) arrow_159774573e_indi (fequal nat) h) n)) % 12.22/12.38 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.22/12.38 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.38 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.22/12.38 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.22/12.38 (combb (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.38 (fun arrow_411405190le_alt % 12.22/12.38 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool))) % 12.22/12.38 arrow_159774573e_indi arrow_1158827142_above p) % 12.22/12.38 c) % 12.22/12.38 e)) % 12.22/12.38 (combc arrow_159774573e_indi arrow_411405190le_alt % 12.22/12.38 (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.38 (combb (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool) % 12.22/12.38 (fun arrow_411405190le_alt (fun (product_prod arrow_411405190le_alt arrow_411405190le_alt) bool)) % 12.22/12.38 arrow_159774573e_indi arrow_276188178_mkbot p) % 12.22/12.38 e))))) % 12.22/12.38 False % 12.22/12.38 Clause #4406 (by superposition #[4405, 218]): Eq False True % 12.22/12.38 Clause #4409 (by clausification #[4406]): False % 12.22/12.38 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------